Question

If $A=\left[\begin{array}{ccc}1& 2& 3\\ 5& 0& 7\\ 6& 2& 5\end{array}\right]$ and $B=\left[\begin{array}{ccc}1& 3& 5\\ 0& 0& 2\end{array}\right],$ then which of the following is defined?

• A. $A+B$
• B. $A^{\prime }{B}^{\prime }$
• C. $AB$
• D. $B^{\prime }{A}^{\prime }$

Answer 1

The correct option is B $A^{\prime }{B}^{\prime }$

Given, order of $A=3\times 3$

Order of $B=2\times 3$

So, $AB$ is not defined.

$A\pm B$ is not defined.

$\Rightarrow$ Order of $B^{\prime }=3\times 2$

Order of $A^{\prime }=3\times 3$

So, $A^{\prime }{B}^{\prime }$ is defined.

Hence, the answer is $A^{\prime }{B}^{\prime }.$